Problem: Solve for $x$ : $ 5|x + 4| + 5 = 4|x + 4| + 2 $
Explanation: Subtract $ {4|x + 4|} $ from both sides: $ \begin{eqnarray} 5|x + 4| + 5 &=& 4|x + 4| + 2 \\ \\ { - 4|x + 4|} && { - 4|x + 4|} \\ \\ 1|x + 4| + 5 &=& 2 \end{eqnarray} $ Subtract ${5}$ from both sides: $ \begin{eqnarray} 1|x + 4| + 5 &=& 2 \\ \\ { - 5} &=& { - 5} \\ \\ 1|x + 4| &=& -3 \end{eqnarray} $ Simplify: $ |x + 4| = -3$ The absolute value cannot be negative. Therefore, there is no solution.